1. Field of the Invention
The present invention relates to the field of magnetic recording channels, and more particularly, to codes for magnetic recording channels.
2. Description of the Related Art
Partial response signaling with maximum likelihood detection (PRML) has been theoretically and experimentally proven to have a substantial performance advantage over the peak detection method for magnetic storage systems.
A description of partial-response (PR) signaling principles is given by P. Kabal and S. Pasupathy, "Partial-Response Signaling," IEEE Transactions on Communications, vol. COM-23, no. 9, pp. 921-934, September 1975. In PR signaling systems, a controlled amount of intersymbol interference is allowed in the responses received by the detector.
Recently, PR has been widely applied to magnetic recording systems, replacing the peak detection method. In partial response signaling, more than one sample of the input signal has a non-zero value, as opposed to peak detection in which only one sample of the received input signal is assumed to be different than zero.
PR signaling receivers are usually combined with maximum-likelihood (ML) sequence detection methods to take advantage of the controlled amount of intersymbol interference from ML methods. The asymptotically optimal method of implementing the ML detection technique is by the use of the Viterbi algorithm described in: A. J. Viterbi, "Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm," IEEE Transactions on Information Theory, Vol. IT-13, No. 2, pp. 260-269, April 1967, and G. D. Forney, Jr, "The Viterbi Algorithm," Proceedings of the IEEE, Vol. 61, No. 3, pp. 268-278, March 1973.
Applying the principles of PRML signaling and detection in communication channels and storage systems has been described in: G. D. Forney, Jr, "Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference," IEEE Transactions on Information Theory, Vol. IT-18, No. 3, May 1972; H. Kobayashi, "Application of Probabilistic Decoding to Digital Magnetic Recording," IBM Journal of Research and Development, vol. 15, pp. 64-74, January 1971; and K. Nishimura and K. Ishii, "A Design Method for Optimal Equalization in Magnetic Recording Channels with Partial Response Channel Coding," IEEE Transactions on Magnetics, vol. MAG- 19, pp. 1719-1721, September 1983.
PRML read channels have been used to replace peak detection channels due to their increased linear density. PRML systems equalize the received signal to the target waveform, which describes the class of the system. The commonly used channels are represented as (1-D)(1+D).sup.n, where n=1 corresponds to a class-4 (PR4) channel, n=2 corresponds to an extended PR4 (EPR4) channel, and n=3 corresponds to an E.sup.2 PR4 channel. D denotes a unit sample delay.
The equalized sequence is sent to a Viterbi detector which estimates the channel input sequence based on the set of noisy observations which are a set of recorded sequences possibly altered due to noise. The detector takes this set of possible input sequences and calculates which one has the highest probability of being the correct one.
Recently, several codes have been proposed for partial response signaling that by coding constraints eliminate the most common error events. It was shown in R. Karabed and N. Nazari, "Analysis of Error Sequences for PRML and EPRML Signaling Performed over Lorenzian Channel," pp. 368-373, Globecom '96, that at high user densities of the recording, the most common errors are produced by the failure to detect a sequence of three or more transitions. Maximum transition run (MTR) codes, proposed by J. Moon and B. Brickner, "Maximum Transition Run Codes for Data Storage Systems," IEEE Transactions on Magnetics, vol. 32, no. 5, September 1996, eliminate all the possible sequences of three or more transitions, thus resulting in reduced code density (rate 8/10). The other codes, such as Z. Keirn et al, "Experimental Performance Comparison of FTDS/DFE Detectors: 8/9 (0,k) vs. 4/5 MTR Codes," InterMag 97, allow sequences of three transitions (tribits) at specific locations within each codeword, such as at the start on either odd or even numbered bits, but not both.
The code proposed by W. Bliss, "An 8/9 Rate Time-Varying Trellis Code for High Density Magnetic Recording," InterMag 97, allow tribits at different positions within a codeword, which result in a mapping of 16 user bits to 18 bits of coded channel data. The burst error propagation of this code is 4 bytes.
The code introduced by P. H. Siegel, E. Soljanin, A. Young, "Rate 8/9 Trellis Code for E2PR4," University of at San Diego--Center for Magnetic Recording Research Seminar, May 1997, implements 8/9 code that independently maps 8 input bits into 9 code bits with the similar constraints. This code limits the propagation of error to two user bytes. The major disadvantage of this code is that its restriction on allowed tribits requires an implementation of the Viterbi detector that is variable in time, significantly increasing the detector's complexity and reducing its speed.